:mod:`klefki.curves`
====================

.. py:module:: klefki.curves


Subpackages
-----------
.. toctree::
   :titlesonly:
   :maxdepth: 3

   bns/index.rst


Submodules
----------
.. toctree::
   :titlesonly:
   :maxdepth: 1

   arith/index.rst
   baby_jubjub/index.rst
   bls12_381/index.rst
   secp256k1/index.rst


Package Contents
----------------

Classes
~~~~~~~

.. autoapisummary::

   klefki.curves.EllipticCurveBabyJubjub
   klefki.curves.ECGBN128
   klefki.curves.ECGBLS12_381
   klefki.curves.EllipticCurveGroupSecp256k1



.. py:class:: EllipticCurveBabyJubjub(*args)

   Bases: :class:`klefki.algebra.groups.EllipticCurveGroup`

   Twisted Edwards Form (standard)
   y^2 = x^3 + Ax^2 + x
   Montgomery Form
   By^2 = x^3 + A x^2 + x

   .. attribute:: A
      

      

   .. attribute:: B
      

      

   .. attribute:: N
      

      

   .. method:: op(self, g)

      The Operator for obeying axiom `associativity` (2)



.. py:class:: ECGBN128(*args)

   Bases: :class:`klefki.algebra.groups.ecg.PairFriendlyEllipticCurveGroup`

   y^2 = x^3 + A * x + B

   .. attribute:: A
      

      

   .. attribute:: N
      

      

   .. attribute:: F
      

      

   .. method:: op(self, g)

      The Operator for obeying axiom `associativity` (2)


   .. method:: twist(self)


   .. method:: twist_FP_to_FP12(cls, x, y)
      :classmethod:


   .. method:: twist_FP2_to_FP12(cls, x, y)
      :classmethod:


   .. method:: linefunc(P1, P2, T)
      :staticmethod:


   .. method:: miller_loop(cls, Q, P)
      :classmethod:


   .. method:: pairing(cls, P, Q)
      :classmethod:

      e(P, Q + R) = e(P, Qj * e(P, R)
      e(P + Q, R) = e(P, R) * e(Q, R)


   .. method:: is_on_curve(self)


   .. method:: B(F=BN128FP)
      :staticmethod:


   .. method:: lift_x(cls, x)
      :classmethod:



.. py:class:: ECGBLS12_381(*args)

   Bases: :class:`klefki.algebra.groups.ecg.PairFriendlyEllipticCurveGroup`

   y**2 = x**3 + 4

   .. attribute:: A
      

      

   .. attribute:: N
      

      

   .. attribute:: F
      

      

   .. method:: op(self, g)

      The Operator for obeying axiom `associativity` (2)


   .. method:: twist(self)


   .. method:: twist_FP_to_FP12(cls, x, y)
      :classmethod:


   .. method:: twist_FP2_to_FP12(cls, x, y)
      :classmethod:


   .. method:: linefunc(P1, P2, T)
      :staticmethod:


   .. method:: miller_loop(cls, Q, P)
      :classmethod:


   .. method:: pairing(cls, P, Q)
      :classmethod:

      e(P, Q + R) = e(P, Qj * e(P, R)
      e(P + Q, R) = e(P, R) * e(Q, R)


   .. method:: is_on_curve(self)


   .. method:: B(F=BLS12_381FP)
      :staticmethod:


   .. method:: lift_x(cls, x)
      :classmethod:



.. py:class:: EllipticCurveGroupSecp256k1(*args)

   Bases: :class:`klefki.algebra.groups.EllipticCurveGroup`

   y^2 = x^3 + A * x + B

   .. attribute:: N
      

      

   .. attribute:: A
      

      

   .. attribute:: B
      

      

   .. method:: op(self, g)

      The Operator for obeying axiom `associativity` (2)


   .. method:: lift_x(cls, x: FiniteField)
      :classmethod: